Where are photons created in parametric down conversion? On the control of the spatio-temporal properties of biphoton states

In spontaneous parametric down-conversion photons are known to be created coherently and with equal probability over the entire length of the crystal. Then, there is no particular position in the crystal where a photon pair is created. We make the seemingly contradictory observation that we can control the time delay with the crystal position along the propagation direction. We resolve this contradiction by showing that the spatio-temporal correlations critically affect the temporal properties of the pair of photons, when using a finite detector size. We expect this to have important implications for experiments that require indistinguishable photons.